What are the factors of quadratic equation 6x^2+9x-12=0 and also find the roots. Using quadratic formula and factorisation method

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Solution

$G i v e n q u a d r a t i c e q u a t i o n i s 6 x^{2} + 9 x - 12 = 0 F i n d i n g t h e r o o t s u \sin g q u a d r a t i c f o r m u l a 6 x^{2} + 9 x - 12 = 0 \Rightarrow 3 (2 x^{2} + 3 x - 4) = 0 \Rightarrow 2 x^{2} + 3 x - 4 = 0 \Rightarrow x = \frac{- 3 \pm \sqrt{(3)^{2} - 4 \times 2 \times (- 4)}}{2 \times 2} = \frac{- 3 \pm \sqrt{41}}{4} = \frac{- 3 \pm 6.40}{4} H e n c e x = \frac{3.40}{4} = 0.85 o r \frac{- 9.40}{4} = - 2.35 H e n c e f a c t o r s o f t h e q u a d r a t i c e q u a t i o n a r e (x - 0.85) a n d (x + 2.35) A n d t h e r o o t s a r e 0.85 a n d - 2.35$

Note:- It is very difficult to find the factors by factorisation method since roots are typical.

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